On an Implementation of the One-Sided Jacobi Method with High Accuracy

The one-sided Jacobi method for performing singular value decomposition can compute all singular values and singular vectors with high accuracy. Additionally, the computation cost is insignificant for comparatively small matrices. However, in the case of the conventional implementation in Linear Algebra PACKage, the subroutine may not be able to compute a singular vector with sufficient orthogonality. To avoid this problem, we propose a novel implementation of the one-sided Jacobi method. In the proposed implementation, a Givens rotation with high accuracy and fused multiply-accumulate are adopted.